SOLUTION: To measure the volume of loudness of a sound, the decibel scale is used. The loudness L in decibels (db) of the sound is given by: L =10 log I/I0 where I is the intensity of the so

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: To measure the volume of loudness of a sound, the decibel scale is used. The loudness L in decibels (db) of the sound is given by: L =10 log I/I0 where I is the intensity of the so      Log On


   

Question 251335: To measure the volume of loudness of a sound, the decibel scale is used. The loudness L in decibels (db) of the sound is given by: L =10 log I/I0 where I is the intensity of the sound.
Solve: The band Strange Folk performed in Burlington VT and reached sound levels of 111 db. What is the intensity of the sounds? This is my answer, but my teacher says I did it wrong. Here's what he wrote:
You have made some errors on this question.
--------------------------
L =10 log I/I0
111 = 10 log (l/10)
--------------------------
should be
L =10 log I/I0
111 = 10 log (l/10^(-12)
11.1=log I - log 10^ (-12)
Now solve for I
Thanks!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
It took me a while to understand what was going on. The equation is
L+=+10log%28%28I%2FI%5B0%5D%29%29
Those are i's in the logarithm, not 1's. And the zero in the logarithm is a subscript, not the digit of a number. I think this is where you got confused. (I know this is where I got confused when I first looked at the problem.)

Since I%5B0%5D+=+10%5E%28-12%29, your teacher's solution:
L+=10log%28%28I%2FI%5B0%5D%29%29
111+=+10log%28%28I%2F10%5E%28-12%29%29%29
11.1=log%28%28I%29%29+-+log%28%2810%5E%28-12%29%29%29
is correct so far.

And, as your teacher says, we still need to solve for I. Solving for I means we have to get an equation we I is by itself on one side.

We can start by finding the log%28%28+10%5E%28-12%29%29%29/ If we understand logarithms we will know that this must be -12. If you don't see this:
  • Ask your calculator
  • Use the property of logarithms, log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29, to rewrite log%28%28+10%5E%28-12%29%29%29 as -12%2Alog%28%28+10%29%29. And since log%28%2810%29%29+=+1 by definition this becomes -12.

Our equation is now:
11.1=log%28%28I%29%29+-+%28-12%29
or
11.1=log%28%28I%29%29+%2B+12
Next we can subtract 12 from each side:
-0.9+=+log%28%28I%29%29
If you know how to do inverse logarithms on your calculator you can find "I" now. If not, then we can rewrite this in exponential form:
10%5E%28-0.9%29+=+I
Now we can find "I" by using our calculators to raise 10 to the -0.9 power. (I'll leave this step up to you.)